Question

If a +b + c = 15 and ab +bc + ac = 60, then find the value of a 2 + b 2 + c 2?

Answer 1

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Answer 2

The value of a² + b² + c² = 105

Given :

a + b + c = 15 and ab + bc + ac = 60

To find :

The value of a² + b² + c²

Formula :

$\sf {a}^{2} + {b}^{2} + {c}^{2} = {(a + b + c)}^{2} - 2ab - 2bc - 2ca$

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that

a + b + c = 15 and ab + bc + ac = 60

Step 2 of 2 :

Find the value of a² + b² + c²

a² + b² + c²

$\sf = {(a + b + c)}^{2} - 2ab - 2bc - 2ca$

$\sf = {(a + b + c)}^{2} - 2(ab + bc + ca)$

$\sf = {(15)}^{2} - 2 \times 60$

$\sf = 225 - 120$

$\sf = 105$

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